The paper introduces an augmented adaptive unscented Kalman filter (KF). The proposed novel technique is suitable to simultaneously estimate both the diagonal process noise covariance matrix and the unknown inputs, thus combining previously reported KF estimators for unknown inputs (dual or joint KF) and for covariance matrices (adaptive KF). A selective scaling method is also introduced to improve the convergence property of the suggested KF. The development of the novel KF is also motivated by a specific estimation problem related to crane systems. Cranes represent a special class of weight handling equipment as they are underactuated and described by nonlinear dynamics such that the load present oscillatory behavior. In addition to the increasing need for their automation in various industrial fields, these features also make them a benchmark system in control engineering with numerous control laws reported in the literature for sway elimination and trajectory tracking. A common issue to realize most of the advanced control laws on real, eventually industrial size cranes is the necessity to know the sway angle and frictions on the configuration variables. It is shown in simulation and also with real experiments on a reduced size overhead crane system that the suggested KF is suitable to estimate both the sway angles and the frictions.

Most of the advanced nonlinear control strategies reported in the literature for underactuated mechanisms, such as overhead cranes, require the knowledge of all state variables. For cranes, the state vector includes variables related to the load sway and its velocity. The flatness property of crane-like systems can be exploited to solve both motion planning and tracking problems, so that the load (whose coordinates are included in the set of the flat outputs) exponentially follows a rapid reference trajectory. However, unmodeled friction phenomena and limitations on the direct measurement of sway-related state variables usually impede the practical implementation of flatness-based control laws. This paper proposes the use of an adaptive unscented Kalman filter to estimate friction forces and unmeasured state variables. The convergence of the filter is improved using a novel technique, called condition-based selective scaling. The performance of the suggested scheme is verified through a set of computer simulations on a 2D overhead crane system.

The paper defines a time-scaling scheme such that the scaling function depends on the state variables of the system and on an external variable referred to as the time-scaling input. The system evolving according to the scaled time has thus one more input variable compared to the original system. This time- scaling scheme is applied to the kinematic car with one input, namely the steering angle. The longitudinal velocity of the car is a measurable external signal and cannot be influenced by the controller. Using an on-line time-scaling, which is driven by the longitudinal velocity of the car, by a time-scaling output of the tracking controller, and by their time derivatives up to the second order, one can achieve exponential tracking of any sufficiently smooth reference trajectory with non-vanishing velocity, similar to the two-input differentially flat model of the kinematic car. The time derivatives of the longitudinal velocity and the time-scaling output are no longer necessary if one designs the tracking controller for the linearized error dynamics around the reference path.

The rapidly exploring random tree (RRT) algorithm is a randomized path planning method specifically designed for robots with nonholonomic constraints. This method builds a tree during the calculations and the path is searched in this tree. To solve special, more involved problems (e.g. moving through a narrow passage) the usage of a key configuration is suggested. A key configuration helps to find the path from the start to the goal position. This paper gives a method to use key configurations in the RRT method